High-Level Synthesis (HLS) excels at handling compute-intensive loops with straightforward control but struggles to identify parallelism in kernels with complex and irregular control-flow. To address this, novel scheduling techniques based on speculation have been introduced. While these methods outperform traditional static scheduling, they also introduce significant area overhead, particularly in the rollback control logic. Optimizing the cost of this rollback control logic remains an open challenge. In this work, we show how it is possible to simplify and/or eliminate rollback logic using a combination of static analysis and linear programming. Our results show improvements in both execution throughput and area cost.